Economics 313 Mathematics
for Economists
J.R. Carter
Spring 2008
Text:
Carl P. Simon and Lawrence
Blume, Mathematics for Economists
(New York: Norton, 1994).
Reading Selections From:
Alpha C. Chiang, Fundamental Methods of Mathematical
Economics, 3d ed. (New York:
McGraw-Hill,1984).
Jeffrey Baldani, James
Bradfield, and Robert Turner, Mathematical
Economics
(Ft. Worth: Dryden Press, 1996).
Cliff J. Huang and Philip S.
Crooke, Mathematics and Mathematica for
Economists (Malden, MA: Blackwell
Publishers, 1997).
George G. Judge et al., Introduction to the Theory and Practice of
Econometrics,
2d ed. (New York: Wiley, 1988).
Knut Sydsaeter and Peter J.
Hammond, Mathematics for Economic
Analysis (Englewood Cliffs, NJ:
Prentice-Hall, 1995).
Richard E. Williamson and
Hale F. Trotter, Multivariable Mathematics,
3d ed. (Upper Saddle River, NJ: Prentice
Hall, 1996).
Ronald J. Wonnacott and
Thomas H. Wonnacott, Econometrics, 2d
ed.
(New York: John Wiley, 1979).
Most selections that are not
distributed in class are available on ERES with password econ313.
Graded Assignments:
Problem Sets 10%
First Exam February 26 30%
Second Exam April 3 30%
Final Exam May 6 30%
Late
problem sets are accepted with penalty until answer sheets are
distributed. Exemptions from problem
sets and midterm exams require a note from your class dean. Makeup exams are not given; assignment
weights are redistributed. Exams,
including the final, must be taken at the appointed time. As described
by the College’s academic honesty policy, cheating and collusion on exams are
prohibited.
Provisional Course Outline (with additional applications in problem
sets):
I. Introduction and Review
Course Introduction
Application: Optimization, Equilibrium, and Comparative
Statics in a Linear Market Model
Baldani et al., Chap. 2.5,
"Profit Maximization:
Duopoly," pp. 47-53 (optional).
Basic Math and Calculus
(Reviewed by Student)
Chap. 2, pp. 10-34.
Chap. 5, pp. 82-92.
Baldani et al., Appendix 1,
"Calculus Review," pp. 20-29.
II. Linear Systems and Matrix Algebra
Introduction
Chap. 6, pp. 107-108.
Solving Linear Systems by
Gauss-Jordan Elimination
Chap. 7, pp. 122-128,
129-140.
Matrices and Matrix
Operations
Transpose, Identity, and
Inverse Matrices
Chap. 8, pp. 153-166,
180-181.
Vector Geometry, Linear Independence,
and Rank
Chap. 10, pp. 199-208.
Wonnacott and Wonnacott,
Chap. 14.1, "The Geometric Interpretation of Vectors," pp. 376-389.
Chap. 10, pp. 209-220.
Chap. 11.
Nonsingularity and
Determinants
Chap. 9, pp. 188-193.
Chap. 26, pp. 726-734.
Inverting Matrices with
Elementary Row Operations and with Adjoints
Solving Square Systems by
Matrix Inversion and Cramer's Rule
Chap. 8, pp. 162-172.
Chap. 9, pp. 194-196.
Chap. 26, pp. 735-738.
Application: Duopoly Equilibrium Revisited
Baldani et al., Chap. 4.5,
"A Simple Model of Duopoly," and Chap. 4.6, "Duopoly with
Nonzero Conjectural Variations," pp. 111-115.
III. Vector Calculus
Introduction
Closed, Bounded, Compact,
and Convex Sets
Sydsaeter and Hammond, Chap.
17.2, "A Dash of Topology,"
pp. 603-605.
Vector Functions and
Vector-Valued Functions
Chap. 13, pp. 273-277,
287-292.
Jacobian Derivatives: Affine Approximations, First-Order
Differentials, and Gradients
Chap. 14, pp. 307-312,
323-326.
Chap. 14, pp. 319-322.
Williamson and Trotter, Chap.
5.4A, "Directional Derivatives,"
pp. 170-172.
Chain Rule Generalized to
Vector and Vector-Valued Functions
Williamson and Trotter,
Chap. 6.2, "The Chain Rule,"
pp. 195-204.
Implicit Function Theorem
Chap. 15, pp. 334-341,
342-350, 350-358.
Williamson and Trotter,
Chap. 6.3, "Implicit Differentiation,"
pp. 211-218.
Application: Comparative Statics of a Single-Commodity
Market
Matrix Differentiation
Judge et al., Appendix A.17,
"Vector and Matrix Differentiation,"
pp. 967-969.
IV. Unconstrained Optimization
One-Variable Optimization
(Reviewed by Student)
Chap. 3, pp. 51-57.
First-Order Conditions for
Local Optimum
Chap. 17, pp. 396-398.
Quadratic Approximations,
Second-Order Differentials, and Quadratic Forms
Chap. 16, pp. 375-385.
Second-Order Conditions for
Local Optimum
Chap. 17, pp. 398-400.
Convexity, Concavity, and
Global Optimum (optional)
Chap. 21, pp. 505-522.
Chap. 17, pp. 402-404.
Chiang, Chap. 11.5,
"Second-Order Conditions in Relation to Concavity and Convexity," pp.
337-340.
Application:
Comparative Statics of Factor Demand
V. Constrained Optimization
Introduction to
Lagrange-Multiplier Method
First-Order Conditions for
Local Constrained Optimum
Chap. 18, pp. 411-423.
Economic Interpretation of
the Lagrange Multiplier
Chap. 19, pp. 448-450.
Second-Order Conditions for
Local Constrained Optimum
Chap. 16, pp. 386-391.
Chap. 19, pp. 457-463.
Huang and Crooke, Chap.
11.2.3, "Sufficient Conditions," pp. 427-434 (optional, with
different notation for principal minors).
Quasiconcavity,
Quasiconvexity, and Global Constrained Optimum (optional)
Chap. 21, pp. 522-533.
Application: Pure Public Goods and the Crowding-Out
Hypothesis
Application: Least-Cost Input Combination (optional)
Chap. 22, pp. 557-564.
Application: Compensated Demand, Marshallian Demand, and
the Slutsky Equation (optional)
Chap. 22, pp. 544-557.
VI. Exponents and Logarithms (recommended for
future study)
Exponential Functions
Continuous Compounding and
the Number e
Logarithms
Properties and Derivatives
of Exponential and Logarithmic Functions
Application: Optimal Holding Time
Chap. 5
VII. Value Functions, Envelope Theorem, and
Duality (recommended for future study)
Value Functions
Envelope Theorem for
Unconstrained Optimization
Application: Price-Taker Maximum Profit Function
Baldani et al., Chap. 13,
"Value Functions and the Envelope Theorem:
Theory," pp. 308-314.
Envelope Theorem for
Constrained Optimization
Application: Indirect Utility Function
Baldani et al., Chap. 13,
"Value Functions and the Envelope Theorem:
Theory," pp. 314-317, 319-321.
Duality and the Slutsky
Equation Revisited
Baldani et al., Chap. 14,
"Value Functions and the Envelope Theorem:
Duality and Other Applications," pp. 324-329, 336-339.